# Exploiting Verification-Generation Gap: Test-Time Reinforcement Learning with Confidence-Conditioned Verification

arXiv: https://arxiv.org/abs/2606.03608 · HTML: https://mlsanity.com/paper/2606.03608/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 36 of its 39 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- Deep reinforcement learning methods / [RL training of language and agent models](https://mlsanity.com/deeprl/rl-training-of-language-and-agent-models/)

## Builds on (most cited first, 30 of 36)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [OctoThinker: Mid-training Incentivizes Reinforcement Learning Scaling](https://mlsanity.com/paper/2506.20512/) (2025)
- [Forest-of-Thought: Scaling Test-Time Compute for Enhancing LLM Reasoning](https://mlsanity.com/paper/2412.09078/) (2024)
- [Pass@K Policy Optimization: Solving Harder Reinforcement Learning Problems](https://mlsanity.com/paper/2505.15201/) (2025)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [Can Large Reasoning Models Self-Train?](https://mlsanity.com/paper/2505.21444/) (2025)
- [Evolving Language Models without Labels: Majority Drives Selection, Novelty Promotes Variation](https://mlsanity.com/paper/2509.15194/) (2025)
- [SPC: Evolving Self-Play Critic via Adversarial Games for LLM Reasoning](https://mlsanity.com/paper/2504.19162/) (2025)
- [ETTRL: Balancing Exploration and Exploitation in LLM Test-Time Reinforcement Learning Via Entropy Mechanism](https://mlsanity.com/paper/2508.11356/) (2025)
- [Co-rewarding: Stable Self-supervised RL for Eliciting Reasoning in Large Language Models](https://mlsanity.com/paper/2508.00410/) (2025)
- [Learning to Self-Verify Makes Language Models Better Reasoners](https://mlsanity.com/paper/2602.07594/) (2026)
- [Incentivizing LLMs to Self-Verify Their Answers](https://mlsanity.com/paper/2506.01369/) (2025)
- [RESTRAIN: From Spurious Votes to Signals -- Self-Driven RL with Self-Penalization](https://mlsanity.com/paper/2510.02172/) (2025)
- [SPINE: Token-Selective Test-Time Reinforcement Learning with Entropy-Band Regularization](https://mlsanity.com/paper/2511.17938/) (2025)
- [CoVerRL: Breaking the Consensus Trap in Label-Free Reasoning via Generator-Verifier Co-Evolution](https://mlsanity.com/paper/2603.17775/) (2026)
- [What If Consensus Lies? Selective-Complementary Reinforcement Learning at Test Time](https://mlsanity.com/paper/2603.19880/) (2026)

## Built on by (most cited first, 1 of 1)

- [Sharpen Before You Adapt: Data-Free Entry-State Sharpening for Test-Time Reinforcement Learning](https://mlsanity.com/paper/2610.00903/) (2026)

## Abstract (arXiv)

Test-time reinforcement learning has emerged as a promising paradigm for enhancing the complex reasoning abilities of large language models in a completely label-free manner. Despite existing studies focusing on Pass@1 performance, optimizing Pass@k remains under-explored yet critical in label-free settings, which measures generation coverage for sustained exploration. Optimizing Pass@k in label-free setting is highly non-trivial, as directly applying the Pass@k advantage designs effective for RLVR yields unsatisfactory performance. Through in-depth empirical analysis, we discover the root causes hindering performance: pseudo-label estimations for low-confidence samples have a high probability of being incorrect, while candidate answers for high-confidence samples suffer from severe diversity collapse. To overcome these hurdles, we propose TTRL-CoCoV (Test-Time Reinforcement Learning with Confidence-Conditioned Verification), a novel confidence-adaptive framework that expands Pass@k coverage and improves Pass@1 performance. Based on our key insight that verification capability generally leads generation capability, TTRL-CoCoV employs a confidence-conditioned mechanism: for high-confidence samples, it bootstraps verifier and applies an exploration-enhancing reward to prevent diversity collapse; for low-confidence samples, it delegates pseudo-label selection to the verifier to filter incorrect pseudo-labels; and for medium-confidence samples, it bypasses verification entirely. Extensive experiments demonstrate that TTRL-CoCoV outperforms the best competing methods across 6 widely-recognized benchmarks, achieves average absolute gains of +9.8% in Pass@1 and +18.7% in Pass@16 over TTRL, and even achieves absolute Pass@1 improvements of up to +5.0% across multiple reasoning benchmarks when compared against fully supervised RL methods. Our code repository: https://github.com/shanjf666/CoCoV.